The cable cars in San Francisco are pulled along their tracks by an underground

Question

The cable cars in San Francisco are pulled along their tracks by an underground steel cable that moves along at 9.5 mph . The cable is driven by large motors at a central power station and extends, via an intricate pulley arrangement, for several miles beneath the city streets The length of a cable stretches by up to 100 ft during its lifetime. To keep the tension constant, the cable passes around a 1.5-m-diameter "tensioning pulley" that rolls back and forth on rails, as shown in the figure. A m = 1900 kg block is attached to the tensioning pulley's cart, via a rope and pulley, and is suspended in a deep hole. (Figure 1) What is the tension in the cable car's cable? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

mass of pulley is attached to acart =1900kg

from given information

the cart does not accelerate, the forces acting on it must be balanced.

since the pulley on the right moves at constant speed, it does not accelerate.

the tension in the cable is the same at the top and the bottom.

so,

tension in the cable at top + tension in the cable at bottom = weight of 1900kg

2T= mg

T = mg / 2 = 1900 *9.8 / 2 =9310 N

the tension in the cable T=9310 N

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